The persistent identifier that works regardless of version changes is taken from the WebDAV link that you can find when you View Details on the document. However, it breaks when you change the file name.

The persistent identifier that works regardless of file name changes is taken from the URL link that you can find when you View Details on the document. However, it won't return anything other than that version of the file.

You may be able to create a web service/script that given the unique ID of a version of the file, always returns the most recent version of the file, regardless of name.